EP2827769A1 - Methods and systems for brain function analysis - Google Patents
Methods and systems for brain function analysisInfo
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- EP2827769A1 EP2827769A1 EP13764042.1A EP13764042A EP2827769A1 EP 2827769 A1 EP2827769 A1 EP 2827769A1 EP 13764042 A EP13764042 A EP 13764042A EP 2827769 A1 EP2827769 A1 EP 2827769A1
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- eeg
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- seizure
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
- A61B5/7203—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal
- A61B5/7207—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal of noise induced by motion artifacts
- A61B5/7214—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal of noise induced by motion artifacts using signal cancellation, e.g. based on input of two identical physiological sensors spaced apart, or based on two signals derived from the same sensor, for different optical wavelengths
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
- A61B5/316—Modalities, i.e. specific diagnostic methods
- A61B5/369—Electroencephalography [EEG]
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
- A61B5/25—Bioelectric electrodes therefor
- A61B5/279—Bioelectric electrodes therefor specially adapted for particular uses
- A61B5/291—Bioelectric electrodes therefor specially adapted for particular uses for electroencephalography [EEG]
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
- A61B5/316—Modalities, i.e. specific diagnostic methods
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/40—Detecting, measuring or recording for evaluating the nervous system
- A61B5/4076—Diagnosing or monitoring particular conditions of the nervous system
- A61B5/4094—Diagnosing or monitoring seizure diseases, e.g. epilepsy
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
- A61B5/7221—Determining signal validity, reliability or quality
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/74—Details of notification to user or communication with user or patient ; user input means
- A61B5/742—Details of notification to user or communication with user or patient ; user input means using visual displays
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/74—Details of notification to user or communication with user or patient ; user input means
- A61B5/7475—User input or interface means, e.g. keyboard, pointing device, joystick
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
- A61B5/7203—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal
- A61B5/7207—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal of noise induced by motion artifacts
- A61B5/721—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal of noise induced by motion artifacts using a separate sensor to detect motion or using motion information derived from signals other than the physiological signal to be measured
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
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- A61B5/7235—Details of waveform analysis
- A61B5/725—Details of waveform analysis using specific filters therefor, e.g. Kalman or adaptive filters
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- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
- A61B5/7235—Details of waveform analysis
- A61B5/7253—Details of waveform analysis characterised by using transforms
- A61B5/7257—Details of waveform analysis characterised by using transforms using Fourier transforms
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/08—Feature extraction
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- G06F2218/12—Classification; Matching
Definitions
- the human brain is a very delicate organ that makes possible complex behavioral decision making. I nformation processing within the human brain is so sophisticated and complex that it cannot be accessed entirely even with the advanced technology available today. Once a brain is damaged, it is often very hard to achieve full recovery. The importance of accurate, timely diagnoses of brain abnormality is crucial in many clinical settings including the emergency room (ER) or intensive care unit (ICU) . However, most mental and neurological states are evaluated mainly through interviews and subjective exams based on the subjects' temporary performance at that time. There is no objective quantitative test for evaluating baseline brain f unction. Imaging technologies such as standard magnetic resonance imaging (MRI) show only structure within the brain without providing an indication of dynamic brain function. EEG is the most effective method for evaluating brain function, but interpretation requires interpretation of multichannel graphs based on visual analysis by highly trained experts.
- MRI magnetic resonance imaging
- FIG. 1 is a block diagram illustrating an example of a system for evaluating a condition of a brain in accordance wit h various embodiments of the present disclosure.
- FIGS. 2A and 2B are a flowchart illustrating an example of functionality of the system of FIG. 1 in accordance with various embodiments of the present disclosure.
- FIGS. 3A and 3B are a flowchart illustrating examples of feature extraction, network modeling , and classification of the flowchart of FIG. 2B in accordance with various embodiments of the present disclosure .
- FIG. 4 is a graphical representation of an example of a processor system suitable for implementing the system of FIG. 1 in accordance with various embodiments of the present disclosure .
- Electroencephalography is a technology for measuring the voltage and frequency of electrical activity from neurons in the cerebral cortex.
- Electroencephalogra m (EEG) electrodes can record brainwaves using electrodes attached to the scalp or, through electrodes placed on the surface of the brain (subdural electrodes) or within brain tissue (depth electrodes) using surgical procedures.
- a scalp EEG is a non-invasive procedure which provides useful information about brain state and function. This methodology is used in many fields of neuroscience (e.g. , psychology , epilepsy, brain machine interface, and sleep research) for recording and analyzing brain state and function . It is used widely as a diagnostic tool in clinical neurology to evaluate and monitor brain function and to identify disturbances in the function of the brain caused by a variety of insults to the brain , such as concussion, traumatic injury, stroke, tumor, encephalopathies due to toxins or metabolic
- EEG electrosenory tyrene-semiconductor
- a normal brain generates signals with characteristic frequencies, waveforms and spatial organization. Normal brain electrical activity is remarkably symmetrical over the two cerebral he mispheres. In clinical practice, the EEG is analyzed visually to detect diffuse bilaterally disturbances in ongoing
- the EEG is useful for evaluation of chronic conditions, such as dementia. However, its most important use is in the evaluation of acute or subacute conditions presenting as altered mental status or impaired sensorium, such as stupor or coma.
- EEG recordings Analysis and interpretation of EEG recordings is performed by experts (usually neurologists with training in the interpretation of EEG recordings) based on visual inspection of multichannel recordings displayed as multichannel g raphs of signal voltage over time.
- the spatial temporal patterns of brain electrical activity can be analyzed though quantitative analysis of the spatial and temporal properties of this activity, generating a mathematical model of the activity, analyzing the properties of the model, and comparing those properties to a standard of norms based on the properties of normal individuals of similar age.
- a useful mathematical model for analyzing brain state and function is a network model, based on graph theory. Mathematical analysis of local and global properties allow identification of normal physiological states and allow identification of focal, lateralized or diffuse disturbances in physiological function and states.
- While brief EEG recordings provide useful diagnostic information regarding function and state at the time of recording, analysis of long-term recording is useful for monitoring brain conditions such as level of consciousness, identifying abnormal transients in the signal, such as interictal epileptiform discharges , seizures, acute cerebral ischemia, hypoglycemia or anoxia.
- Analyzing the spatial-temporal dynamics of long-term EEG recording data can be achieved through use of quantitative dynamical network models. This approach can provide diagnostic information pertaining to the physiological states of the brain, and can be used to identify transient pathological conditions.
- the above described approach to network analysis of brain electrical activity can be achieved through computer-based algorithms designed to identify artifact, condition the signal, generate quantitative measures of signal properties from each of multiple EEG channels derived from multiple electrodes placed in standard locations on the scalp, generating a network model, calculating local and global properties of the network and comparing to standard network norms derived from normal subjects. These network properties can be monitored over time and compared with the patient or subject's baseline to detect significant changes in state or development of transient pathological conditions.
- the algorith m can provide detailed quantitative output or can summarize the results and categorize them as normal or abnormal. Abnormalities can be categorized as to focal, lateralized or diffuse, and the anatomical location focal and lateralized abnormalities can be reported.
- This output can be written as a report or depicted as a graph.
- the algorithm can be trained and compared to the interpretation of expert electroencephalographers to optimize the sensitivity and specificity of the algorithm.
- An appendix which is hereby incorporated by reference in its entirety, provides additional information about EEG analysis of brain dynamical behavior. [0011]
- This disclosure presents systems and methods for reliably evaluating a recorded EEG in real time by algorithms and providing an immediate indication of the cerebral condition .
- the acquired EEG data may be evaluated in real time and/or may be stored for subsequent evaluation.
- the system allows EEG data to be recorded and evaluated when no E EG technical personnel or neurological interpreters are readily available, allowing its use as a screening tool to assist physicians when such personnel are not available.
- the original EEG data may also be stored for subsequent visual analysis and/or may be transmitted to remote sites for review and interpretation by experts.
- EEG data can be recorded with small, portable, inexpensive instruments that do not require special shielded facilities or the subject remaining motionless for long periods of time.
- an EEG can be utilized in noisy point-of-care environments, such as Emergency rooms and Intensive Care Units and with subjects who may be uncooperative.
- Portable EEG units can also be utilized in emergency vehicles and in the field.
- FIG. 1 shown is a block diagram illustrating an example of a system 100 for evaluating a condition of a brain.
- the system 100 includes an electrode application module 103, an EEG recording module 106, a signal conditioning module 109, a signal analysis module 1 12 , and a condition classification module 1 15.
- the system 100 may contain an interactive display which may provide, e.g. , step-by-step instructions on electrode placement, establishing connections, preparing the subject and initiating the recording, etc.
- the system 100 allows for rapid acquisition and analysis of EEG signals, measurement of the spatial- temporal characteristics of the signal, analysis of local, regional , and diffuse signal characteristics, characterization of network features of EEG signals, determination of whether or not these EEG characteristics are normal or abnormal, and classification of abnormal EEG recording s to determine whether the abnormalities are local, lateralized, multifocal or diffuse.
- the results may be displayed as in a text and/or graphical format that may be available for immediate use by emergency room personnel, intensive care personnel, and emergen cy medical technicians .
- FIGS. 2A-2B shown is a flowchart illustrating various functions that may be implemented by modules of the system 100.
- an electrode application proc edure may be provided in box 203 by the electrode application m odule 103 fo r rendering on the system display.
- the E EG provides direct information about brain functions through analysis of brain electrical act ivity. Depend ing on the location and the type of the electrodes, EEG signals can reveal different levels of neuronal activity. Numerous scalp EEG electrodes may be applied to a subject to obtain E EG data containing information from brain activity in both temporal and spatial domains.
- the EEG electrodes can include individual elect rodes and/or an array of electrodes that are positioned on the scalp.
- the location of electrode placement on the scalp can follow, e.g. , a 1 0-20 system or other appropriate system as can be appreciated.
- I n the 10-20 system distinct landmarks of the subject's head are first identified and then electrodes are placed at 1 0% or 20% distance intervals along the land marks.
- intracranial electrodes may be utilized .
- the recording i ntegrity and impedan ce of the electrodes are checked in box 206 to determine if there is a problem with the placement and/or operation of the EEG electrodes .
- the problematic electrodes may be indicated in box 209 on the s ystem display and the appropriate application or correction procedure (s) may be provided in box 203. Guiding the operator through simple set-up and operating procedures to obtain a technically adequate EEG recording reduces evaluation errors.
- an EEG is obtained under specified conditions in box 212 by the E EG recording module 106.
- EEGs may be obtained with the subject's eyes open a nd closed or other specified conditions of the subject.
- I nstructions may be rende red for display on the system display to prompt the specified condition (or action) in the monitored subject.
- a subject is usually asked to relax and open eyes for a period of time and then close eyes for another period of time.
- the acquired EEG signals are then processed in box 215. For example, amplification and filtering may be applied to enhance the signal-to-noise ratio (SNR) of the EEG signals.
- SNR signal-to-noise ratio
- Analog EEG signals from the electrodes may also be digitized for communication and storage of the information.
- acceptability of the recording quality of the EEG data is confirmed.
- all channels of the processed EEG signal may be analyzed for the presence of excessive artifacts that may contaminate the EEG data. Criteria for acceptable signal quality may be predefined to ensure acceptable electrode contact, electrode impedance, and minimal contamination by common artifacts.
- EEG data is not acceptable, then the system can return to box 206 to recheck electrode integrity and impedance .
- Common technical proble ms that degrade the recording e.g . , excess muscle or movement artifacts
- Instructions may be provided through the system display to guide the operator in methods to eliminate or attenuate those artifacts before repeating the acquisition of EEG signals in box 212.
- Subsequent recorded EEG data may be re-evaluated and the operator notified of persistent problems, at which time the operator may attempt to obtain further EEG signals or may abort the procedure.
- the digitized data can be stored in a data store or other memory in box 221 .
- the stored EEG data may be transmitted through a wireless or wired network connection (e.g. , cellular, Bluetooth , Ethernet, ere.) for remote evaluation, analysis, and/or confirmation.
- a wireless or wired network connection e.g. , cellular, Bluetooth , Ethernet, ere.
- the acceptable EEG data is further processed and/or filtered by the signal conditioning module 109 to remove common recording artifacts as illustrated in FIG. 2B.
- eye movement artifacts may be detected and removed in box 224
- electromyogram (muscle movement) artifacts may be detected and removed in box 227
- electrode related artifacts such as, e.g. , electromagnetic interference from nearby instruments may be detected and removed in box 230.
- Other artifacts such as, e.g. , 60 Hz line signals and signals produced by mechanical ventilators and other instruments may also be detected and removed from the EEG data by the signal conditioning module 109.
- epochs of data may be examined sequentially for the presence of an artifact.
- a segment contains an excessive artifact, it may then be excluded from subsequent analysis.
- the signal conditioning module 1 09 identifies and discards the artifact-contaminated segments, the remain ing EEG data is evaluated in box 233 to ensure that a useable signal of sufficient duration has been acquired and is available for analysis An initial interpretation may be generated based upon a brief EEG recording (e.g. , 2 to 5 m inutes). If the available data is not long enough for reliable analysis, the system 1 00 will inform the operator and return to box 212 to obtain additional EEG data. If the available EEG data is long enough for analysis or evaluation , the EEG data is processed by the signal analysis modu le 1 12 to extract featu res in box 236.
- the system 100 may also provide an option to continue recording to obtain a complete routine EEG (typically around 20 -30 minutes of recording ) or for continued monitoring the EEG for changes in brain function, such as intermittent seizures, diffuse or focal ischemia , and changes in alertness or level of consciousness .
- the system 1 00 may be placed i n a monitoring mode in wh ich epochs of the EEG are analyzed as they are acquired to detect transient abnormalities or state changes in the subject.
- a continuous or intermittent analysis may be provided graphically and/or a summary report may be provided intermittently at specified intervals.
- the interval between reports can be a defau lt interval (e. g. , every 1 0 m inutes) or can be an interval that is selected by the operator.
- the extracted features of the multichannel EEG data from box 236 may be used to provide a quantitative description of the spatiote mporal characteristics of the signals, including local and regional cha racteristics, inter-hemispheric asymmetries, and local and global network connectivity characteristics.
- the extracted features may be, e.g. , linear, non -linear, univariate, or bivariate statistics.
- the extracted features from box 236 may be provided as inputs for network modeling in box 239 and for classification of the cerebral condition in box 245 of the condition classification module 1 1 5. For example, if the featu re is univariate, such as entropy, each EEG channel wi ll have a feature time series.
- the network modeling in box 239 is implemented based upon the degree of association between these univariate features between channels. If the feature is bivariate (or a relationship between two channels), the network modeling in box 239 may be directly imple mented through the values of bivariate features. After the network model has been constructed in box 239, network features may be extracted in box 242 from the network model and provided to the condition class ification module 1 1 5 for classification in box 245. Classification of the cerebral condition can be more precise by including the extracted network features in the evaluation .
- Classification of the cerebral condition in box 245 may be based, at least in part, upon comparison of extracted features from boxes 236 and 242 by comparison with established no rms to determine if they indicate a normal condition within normal limits or an abno rmal condition .
- the condition classification module 1 15 anal yzes EEG signals through a network perspective.
- the functional network reflects the connectedness among brain regions in terms of neuron activity.
- the brain functional network may be represented as a graph by defining vertices and edges in the EEG data.
- EEG channe ls are designated as the vertices of a graph
- an edge between two vertices signifies a functional connection between two EEG channe ls.
- a larger correlation between two EEG chan nels indicates the presence of an edge between the channels.
- Edges may also be values quantifying how well the two vertices correlate in weighted graphs . Applying graph theoretical analysis to EEG data can reveal topological characteristics of the neural network and brain functional network featu res.
- the cerebral condition is determined to be abno rmal, then the location of abnormal features (e.g. , local or focal, lateralized, or diffuse bilateral) and/or the severity of the abnormality (e.g. , mild, moderate, or severe) may be identified in box 248.
- the condition may be identified as abnormal diffuse bilateral, abnormal left hemisphere, or abnormal right hemisphere with slowing, seizures, and/or amplitude disturbance.
- An indication of the classification results may then be generated in box 251 for rendering on the system display. For example, a graphic display of the original EEG signal, local signal properties, inter-hemispheric asymmetries, local network features, and/or global network features may be generated .
- a warning may be generated when an abnormal condition has been indicated.
- a summary (or report) of findings may be provided in several forms which may be selected by the user.
- a default condition may provide a report labeled as normal or indicating the determined abnormal category classification (e.g. , mildly abnormal , left hemisphere).
- a visual display of the anatomical location of the abnormalities may be provided gra phically, using a color bar, grey scale or other graphic display to indicate the severity of the abnormalities.
- Other graphical displays which provide maps of one or more individual signal property may also be viewed.
- the results of the classifications may also be stored in box 251 for later access or retrieval to further evaluation, interpretations, and validation.
- FIGS. 3A and 3B shown are a flowchart illustrating examples of feature extraction, network modeling, and classification of the flowchart of FIG. 2B.
- EEG data is received for EEG signal feature extraction in box 236.
- local properties may be determined from the EEG data including the univariate feature.
- Kaiser-Teager energy and power in the EEG may be computed for each electrode site and referenced to a common reference electrode (e.g., average, Pz, other).
- implementations may use bipolar pairs and calculate for each pair: Fp1 -F3, F3-C3, C3- P3, P3-01 and analogou s for right side, Fp1 -F7, F7-T3, T3-T5, T5, 01 and analogous for right side.
- Local energy and power properties may be determined for each channel for comparison to predetermined normative values for each channel .
- Abnormality of Teager energy and abnormalities for power would be expected to be either higher or lower than the normative values.
- Abnormalities in the Teager energy to Power ration would be expected to be lower than norms.
- Norms may be derived from EEG recordings obtained from a normal test group, with appropriate age matching, or may be based upon baseline recordings obtained in the same subject (in which case, a change from baseline would be detected).
- the follow local property values may be computed in box 303:
- KTE Kaiser-Teager energy
- the value for each channel may be compared to normal values. If the values are outside of the normal range, the degree of abnormality (e.g., based on standard deviations (s.d.) from the mean) for each electrode channel can be determined.
- the location (left cerebral hemisphere, right cerebral hemisphere or bilateral) and degree of abnormality (1 s.d. > x ⁇ 2 s.d., 2 s.d._ ⁇ x ⁇ 3 s.d, or x > 3. s.d.) can be stored and used in the final evaluation and report.
- Pattern match regularity statistic (PM S).
- One or more measures of signal regularity or signal such as the PMRS may be generated for the entire recorded frequency range as well as for each standard EEG frequency band for each electrode channel and compared to normal values. If the values are outside of the normal range, the degree of abnormality (based on standard deviations from the mean) for each electrode channel can be determined.
- the location (left cerebral hemisphere , right cerebral hemisphere or bilateral) and degree of abnormality (1 s.d. > x ⁇ 2 s.d. , 2 s.d._ x ⁇ 3 s.d, or x > 3.s.d.) can be stored and used in the final evaluation and report.
- approximate entropy may be measu red for the entire recorded EEG frequency range as well as for each of the standard EEG frequency bands for each electrode channel and compared to normal values. If the values are outside of the normal range, the degree of abnormality (based on standard deviations from the mean) for each electrode channel can be determined.
- the location (left cerebral hemisphere , right cerebral hemisphere or bilateral) and degree of abnormality (1 s.d. > x ⁇ 2 s.d. , 2 s.d._ ⁇ x ⁇ 3 s.d, or x > 3. s.d.) can be stored and used in the final evaluation and report.
- Teager energy/power ratios are generated for each channel for entire frequency range between 1 and 30 Hz in box 306.
- the KTE to power ratio may be calculated for the entire recorded frequency range as well as for the standard EEG frequency bands is calculated for each channel and compared to normal values. If the values are outside of the normal range, the degree of abnormality (based on standard deviations from the mean) for each electrode channel can determined.
- the location (left cerebral hemisphere, right cerebral hemisphere or bilateral) and degree of abnormality (1 s.d. > x ⁇ 2 s.d. , 2 s.d._ ⁇ x ⁇ 3 s.d, or x > 3. s.d.) can be stored and used in the final evaluation and report.
- Left-right univariate ratios may then be determined in box 309. Inter- hemispheric symmetry computation may be based upon univariate features. Each of the quantitated measures of signal properties, such as those described above, will be examined for inter-hemispheric symmetry by calculating the ration of the value obtained for each of the electrode channels recorded from the left cerebral hemisphere to the same value obtained for the homologous electrode channel in the right hemisphere.
- bivariate features between all channels may also be determined from the EEG data. Inter-hemispheric symmetry computations may be based upon bivariate features. Bivariate measures can be used to evaluate the relationship of signals obtained from each electrode channel from the left cerebral hemisphere to that of the homologous electrodes from the right cerebral hemisphere. These measures include mutual information, linear or nonlinear correlation, coherence, phase locking index and phase lag index. The analysis can be made for the entire range of recorded frequencies as well as for each standard EEG frequency band.
- a network model may then be generated in box 315 based upon the bivariate feature values from box 312.
- a network model can be generated as a weighted graph , based on one or more of the bivariate measures relating signal properties between each pair of electrodes, such that a measure is generated for each electrode site (node) and all other electrodes in the recording.
- the weighted graph can be converted to a binary graph depicting the node pairs with the strongest association, as defined by one or more bivariate measure, using a threshold in box 318.
- a threshold of 0.75 may be used, such that the resultant binary graph includes 25% of the total electrode pairs; in the case of a full set of electrodes, excluding midline electrodes, as defined by the International 10-20 System of electrode placement, the total number of pairs is 171 and 43 pairs would be selected for the binary network graph .
- global network characteristics of the binary and/or weighted network graphs may be determined . These characteristics include, e.g. , clustering coefficient and minimum path length . These global characteristic values are compared to norms in box 324 to determine whether or not they are within the normal range. If the values are outside of the normal range , the degree of abnormality (based on standard deviations from the mean) for each electrode channel is determined. The location (left cerebral hemisphere, right cerebral hemisphere or bilateral) and degree of abnormality (1 s.d. > x ⁇ 2 s.d. , 2 s.d._ ⁇ x ⁇ 3 s.d, or x > 3.s.d.) will be stored and used in the final evaluation and report.
- characteristics for each node can be defined, based on the following characteristics for each node: degree, path length to
- contralateral homologous electrode and connection strength with contralateral homologous electrode.
- the degree of that node can be compared to the degree for the same electrode (node) in the normative dataset in box 327 and the location of nodes whose properties do not match those of the normative dataset can be determined .
- hubs of the binary and/or weighted network graphs may be identified using one or more criteria for defining hubs, such as degree , betweeness, closeness, and eigen vector centrality. Electrodes which exceed thresholds of the values for each respective measure can be defined as a network hub.
- Network hubs identified in the recording can be compared to a list of hubs obtained from a normative comparison dataset. Hubs present in the subject network which do not correspond to hubs in the normal datasets may be identified and their location determined to be lateralized to one cerebral hemisphere, localized within one cerebral, or present bilaterally. In addition, nodes in the recorded data which are not present in the normative datasets can be identified and localized.
- the path length between each electrode (node) and the homologous node in the contralateral hemisphere may be calculated. Values for each channel pair can be compared to those of the normal dataset and the location of those pairs which differ significantly from the normal datasets can be determined .
- the cerebral condition can be classified in box 245 of FIG. 3B based upon comparison of values from boxes 309 and 312 of FIG. 3A.
- the EEG data may be classified, based on the composite results from all, or a subset, of each individual analysis: (1 ) local univiariate signal properties, (2) inter-hemispheric symmetry computations based on local univariate signal properties, (3) inter-hemisphe ric symmetry based on computations of biviariate signal properties, local network prope rties, and global network properties. If all of these analyses are within acceptable range of normal values, the recording may be classified as normal.
- I n box 333 the bivariate feature of homologous pairs is compared with normal values obtained from the same electrode pairs. If the values are outside of the normal range, the degree of abnormality (based on standard deviations from the mean) for each electrode channel may be determined . The location (left cerebral hemisphere, right cerebral hemisphere or bilateral) and degree of abnormality (1 s.d . > x ⁇ 2 s.d. , 2 s.d ._ ⁇ x ⁇ 3 s.d, or x > 3. s.d.) can be stored and used in the final evaluation and report. I n box 336 of FIG. 3B, univariate ratios from each channel pair will be compared to normal ratios for that channel pair.
- the degree of abnormality (based on standa rd deviations from the mean) for each electrode channel may be determined.
- the location left cerebral he misphere, right cerebral hemisphere or bilateral
- degree of abnormality (1 s.d. > x ⁇ 2 s.d . , 2 s.d._ ⁇ x ⁇ 3 s.d , or x > 3. s.d .) can be stored and used in the final evaluation and report.
- the EEG data will be classified as abnormal and assigned to one of several abno rmal categories in box 248 of FIG. 3B.
- the abnormal categories may be defined as follows: (1 ) left hem isphere abnormality, (2) right hemisphere abnormality, (3) bilateral abnormalities.
- EEG data with bilateral abno rmalities may be further subclassified as (3a) bilateral symmetrical abnormalities, (3b) bilateral abnormalities, left greater than right and (3b) bilateral abnormalities right greater than left.
- the location of the abnormality may be made more precise, indicating the region(s) within the cerebral hemisphere(s) containing the abnormalities (e.g. , left front-temporal abnormality).
- Abnormal EEG data may be further categorized as to the degree of abnormality, based upon a weighted magn itude of prope rty deviations from normal values as well as the num ber of properties which deviate significantly from normal values.
- regions of altered symmetry are identified and the severity determined based upon values from box 333.
- the severity of the abnormality is determined in box 339 based upon values for boxes 324, 327, and 330 of FIG. 3A and box 336 of FIG. 3B.
- the degree of abnormality may be based on standard deviations from the mean the values for each electrode channel. In some cases, a weighed combination of the standard deviations may be used to indicate the degree of abnormality.
- the results of the abnormality identification may be stored in a data store or memory and may be used to generate an indication for the operator of the system 100.
- the system 100 may be used for, but is not limited to, neurological assessment of common neurological presentations such as, e.g. , acute
- Acute and subacute encephalopathies include such disorders as those due to traumatic brain injuries, toxic encephalopathies (e.g. drug or alcohol toxicity), metabolic disorders (e.g. hypoglycemia, hyperglycemia, ketoacidosis, renal failure, hepatic failure, hypoxia, hypercapnea), acute or subacute infections of the brain (such as meningitis, encephalitis, and brain abscess), seizures, status epilepticus, stroke, transient ischemic attacks, and autoimmune disorders affecting the central nervous system.
- toxic encephalopathies e.g. drug or alcohol toxicity
- metabolic disorders e.g. hypoglycemia, hyperglycemia, ketoacidosis, renal failure, hepatic failure, hypoxia, hypercapnea
- acute or subacute infections of the brain such as meningitis, encephalitis, and brain abscess
- seizures status epilepticus, stroke, transient ischemic attacks, and autoimmune disorders
- Information obtained through the system 100 may be used to refine the differential diagnosis, formulate further workup (e.g. imaging procedures) and treatment, and for purposes of triage and referral to appropriate facilities and specialists.
- Other potential uses include brain monitoring to evaluate level of alertness, screening of chronic cerebral disorde rs such as, e.g. , Alzheimer's disease and other chronic dementias, and assessment of excess daytime sleepiness and sleep disorders.
- AMSE altered mental status evaluator
- a unique feature of this application is its utility as a tool to assist physicians in the differential diagnosis of subjects in the hospital with acute unexplained persistent altered mental status (AMS). These subjects are commonly seen in the Emergency Room (ER), Intensive Care Unit (ICU) or hospital wards.
- AMSE provides reliable identification of EEG abnormalities that cause altered mental status including subclinical seizures, diffuse EEG slowing reflecting diffuse encephalopathy and focal EEG slowing reflecting focal brain dysfunction.
- AM SE then generates a report to assist the physician in diagnosis of subjects with altered mental status. These results can rapidly point the physician to the differential diagnostic areas that should receive the most consideration initially (but should not preclude other avenues of investigation). The physician correlates the results with their clinical examination and results of other studies to reach a final accu rate diagnosis m ore quickly.
- the processor system 400 includes at least one processor circuit, for example, having a processor 403 and a memory 406, both of which are coupled to a local interface 409.
- the processor system 400 may comprise, for example, at least one computer or like device.
- the local interface 409 may comprise, for example, a data bus with an accompanying address/control bus or other bus structure as can be
- the processor system 400 includes operator interface devices such as, e.g. , a display device 412, a keyboard 415, and/or a mouse 41 8.
- the operator interface device may be interactive display 421 (e.g. , a touch screen) that provides various functionality for operator interaction with the processor system 400.
- Various sensors such as, e.g. , EEG electrodes 424 may also interface with the processor system 400 to allow for acquisition of EEG signals from a subject.
- the EEG electrodes 424 may be an array of electrodes configured to be positioned about the subject's head.
- an application module 427 such as, e.g. , an electrode application module 103, an EEG recording module 106, a signal conditioning module 109, a signal analysis module 1 2, and a condition classification module 1 5 of FIG. 1 , and/or other applications .
- Also stored in the memory 406 may be a data store 430 and other data .
- an operating system 433 may be stored in the memory 406 and executable by the processor 403.
- any one of a number of prog ramming languages may be employed such as, for example, C, C++, C#, Objective C, Java®, JavaScript®, Perl , PHP, Visual Basic®, Python®, Ruby , Delphi®, Flash®, or other programming languages.
- executable means a program file that is in a form that can ultimately be run by the processor 403.
- executable programs may be, for example, a compiled progra m that can be translated into machine code in a format that can be loaded into a random access portion of the memory 406 and run by the processor 403 , source code that may be expressed in proper format such as object code that is capable of being loaded into a random access portion of the memory 406 and executed by the processor 403, or source code that may be interpreted by another executable program to generate instructions in a random access portion of the memory 406 to be executed by the processor 403, etc.
- An executable program may be stored in any portion or component of the memory 406 includi ng, for example, rando m access memory (RAM), read-only memory (ROM), hard drive, solid-state drive , USB flash drive, memory card , optical disc such as compact disc (CD) or digital versatile disc (DVD), floppy disk, magnetic tape, or other memory components.
- the memory 406 is defined herein as including both volatile and nonvolatile memory and data storage components. Volatile components are those that do not retain data values upon loss of power. Nonvolatile components are those that retain data upon a loss of power.
- the memory 406 may comprise, for example, random access memory (RAM), read-only memory (ROM), hard disk drives, solid-state drives, USB flash drives, memory cards accessed via a memory card reader, floppy disks accessed via an associated floppy disk drive, optical discs accessed via an optical disc drive, mag netic tapes accessed via an appropriate tape drive, and/or other memory components, or a combination of any two or more of these memory components.
- the RAM may comprise, for example, static random access memory (SRAM), dynamic random access memory (DRAM), or magnetic random access memory (MRAM) and other such devices.
- the ROM may comprise, for example, a
- PROM programmable read-only memory
- EPROM erasable programmable read-only memory
- EEPROM electrically erasable programmable read-only memory
- the processor 403 may represent multiple processors 403 and the memory 406 may represent multiple memories 406 that operate in parallel processing circuits, respectively.
- the local interface 409 may be an appropriate network that facilitates communication between any two of the multiple processors 403, between any processor 403 and any of the memories 406, or between any two of the memories 406, etc.
- the local interface 409 may comprise additional systems designed to coordinate this communication, including, for example, performing load balancing.
- the processor 403 may be of electrical or of some other available constru ction.
- the electrode application module 103 may be embodied in software or code executed by general purpos e hardware as discussed above, as an alternative the same may also be embodied in dedicated hardware or a combination of software/general purpose hardware and dedicated hardware. If embodied in dedicated hardware, each can be implemented as a circuit or state machine that employs any one of or a combination of a number of technologies. These technologies may include, but are not limited to, discrete logic circuits having logic gates for implementing various logic functions upon an application of one or more data signals, application specific integrated circuits having appropriate logic gates, or other components, etc. Such technologies are generally well known by those skilled in the art and, consequently, are not described in detail herein.
- FIGS. 2A-2B and 3A-3B show a specific order of execution, it is understood that the order of execution may differ from that which is depicted. For example, the order of execution of two or more blocks may be scrambled relative to the order shown. Also, two or more blocks shown in succession in FIGS. 2A- 2B and 3A-3B may be executed concurrently or with partial concurrence . Further, in some embodiments, one or more of the blocks shown in FIGS. 2A-2B and 3A-3B may be skipped or omitted.
- any number of counters, state variables, warning semaphores, or messages might be added to the logical flow described herein, for purposes of enhanced utility, accounting, performance measurement, or providing troubleshooting aids, efc. It is understood that all such variations are within the scope of the present disclosure .
- any logic or application described herein, including the electrode application module 103, the EEG recording module 106, the signal conditioning module 109, the signal analysis module 1 12, the condition classification module 1 15, and/or application(s), t hat comprises software or code can be embodied in any non-transitory computer-readable medium for use by or in connection with an instruction execution system such as, for example, a processor 403 in a computer system or other system.
- the logic may comprise, for example, statements including instructions and declarations that can be fetched from the computer-readable medium and executed by the instruction execution system.
- a "computer- readable medium” can be any nie m that can contain, store, or maintain the logic or application desc ribed herein for use by or in connection with the instruction execution system.
- the computer-readable medium can comprise any one of many physical media such as, for example, magnetic, optical, or semiconductor media. More specific examples of a suitable computer-readable medium would include, but are not limited to, magnetic tapes, magnetic floppy diskettes, magnetic hard drives, memory cards, solid- state drives, USB flash drives, or optical discs.
- the computer-readable medium may be a random access memory (RAM) including, for example, static random access memory (SRAM) and dynamic random access memory (DRAM), or magnetic random access memory (MRAM).
- RAM random access memory
- SRAM static random access memory
- DRAM dynamic random access memory
- MRAM magnetic random access memory
- the computer-readable medium may be a readonly memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM) , an electrically erasable programmable read-only memory (EEPROM), or other type of memory device.
- ROM readonly memory
- PROM programmable read-only memory
- EPROM erasable programmable read-only memory
- EEPROM electrically erasable programmable read-only memory
- Electroencephalogram is a technology measuring the voltage of activation from a set of neurons within the brain .
- EEG electrodes can record brainwaves from either the scalp or, through invasive procedu res, deeper layers of the brain tissue. Depending on t he location and the type of the electrodes, EEG signals can reveal different levels of neuronal activities.
- Scalp EEG is the least invasive methodology and is, therefore, widely used in many fields of neuroscience including psychology, epilepsy, brain machine interface, and sleep research. EEG has become a more popular means of recording interesting brain activity over the last few decades because improvements in computing power and storage capacity make possible sophisticated analyses of very large amounts of EEG data.
- EEG electrocardiogram
- numerous electrodes can be applied on one subject so that the EEG data have both temporal and spatial information of brain activity.
- the location of electrode placement on a scalp usually follows the 10-20 system. Distinct landmarks of a head are first identified and then electrodes are placed at 10% or 20% distance intervals along the landmarks.
- a tempora ry brain network can be identified. Analyzing long-term EEG recording data can reveal the dynamics of the brain network as the subject goes through many states of mental activity or pathological manifestation.
- EEG data included in this disclosure contain both scalp and intracranial EEGs. All of them are continuous long-term recordings from either Allegheny General Hospital (AGH, Pittsburgh , PA) or the Medical University of South Carolina (MUSC, Charleston, SC).
- EEG recordings were analyzed. All scalp EEG data were recorded using 19 channels and intracranial EEG data used respectively different channels covering the different brain areas depending on the specific case of each epileptic patient. All recordings are from human beings who are older than 18 years old and experienced epileptic or psychological non-epileptic seizures.
- Epilepsy is a brain disorder, instead of a disease, characterized mostly by recurrent and unforeseen interruptions of normal brain function. It has been known from ancient times and was, at one point, attributed to divine intervention until the great Greek physician Hippocrates realized that it was a disorder of the brain. It is also the second most common disorder of the central nervous system and affects about 0.4-1 % of the population. The sudden interru tion of brain function is termed a seizure. Many other physical or psychological sudden and severe events are also called seizures, such as a heart seizure. The meaning of a seizure, going back to its' origin in Greek, is "to take hold".
- An epileptic seizure is the manifestation of epilepsy and is due to abnormally excessive or synchronous neuronal activity in the brain.
- the duration of the manifestation of an epileptic seizure is sometimes called an ictal period.
- Most epileptic seizures can be recorded by the electrodes of an EEG and shown in the EEG data. Through reading and analyzing the epileptic EEG data, more information is gained about the onset pattern and type of epilepsy.
- ictal period one may observe that the synchronous and rhythmic discharges originate from one part of the brain (partial, focal or localization-related seizures) or begin simultaneously in both sides of the hemispheres (generalized seizures).
- Focal seizures after the onset may remain localized within one part of the brain or propagate to the other side of the hemisphere and cause a wider range of synchronous neuronal activity (secondarily generalized seizures). If a seizure is confined to a limited area of the brain, it usually causes relatively mild and transient cognitive, psychic, sensory, motor or autonomic impairment. However, generalized seiz ures cause altered consciousness and accompany a variety of motor symptoms from the jerking of limbs to stiff or convulsive movements of the whole body. During the ictal period of focal seizures, consciousness may be unaffected (simple partial seizures) or be impaired (complex partial seizures). Few patients with focal seizures feel unu sual sensations (auras) when experiencing the beginning stage of an ictal period. Most seizures occur in a nearly unpredictable manner, stressing the patients as well as the people around them.
- GABA Gamma-aminobutyric acid
- AED anti-epileptic drugs
- seizure onset frequencies and severities Although patients have different seizure onset frequencies and severities, seizure types and frequencies did not correlate with the score of quality of life. These study results suggest that the frequency or severity of seizures is not the primary cause of patient depression, but rather the sense of uncertainty regarding seizure onsets and the constant fear of unpredictable ons et. The presence of correct seizure onset warnings should alleviate the degree of depression and increase quality of life by decreasing the amount of uncertainty and offering patients the ability to prepare for seizure onset.
- time series such as wind speed, heart rate, stock exchange price, and EEG signals.
- EEG signals By analyzing a time series, insight may be gained into an array of interesting and complex phenomena.
- a human brain is a complex system that responds simultaneously to many external inputs as well as numerous internal processes. Analysis and quantification of the characteristics of EEG signals offer a window to observe the complex interactions amongst neurons in a brain. For example, in awake and asleep EEG signals, one can recognize that the signals usually have swiftly changing backgrounds. Therefore, EEG signals are usually regarded as non-stationary time series consisting of the many distinct background activities that occur when a subject experiences different phases of psychological events or physiological states. Analyzing and forecasting non-stationary time series have been challenging for researchers.
- Equation 2-1 / denotes the probability mass function and ⁇ denotes a time lag of any size.
- Stationarity in the strict sense is almost impossible in real life. Even a parametric simulated process can have stationarity only theoretically, not to mention a time series recorded from real world signals which have much more complex mechanisms. Although one can hardly have a stationary process in the strict sense, the concept of stationarity may be utilized when studying non-stationary time series because of its convenient statistical properties. A process may be claimed to have stationarity in a wide sense if it has not only a fixed mean and variance but also time-invariant auto-covariance. One reason for keeping the concept of stationarity in a stochastic process is that a parametric model can hardly include all variables that affect the process, not to mention some factors that are beyond the researcher's control.
- One of the crucial parameters for using the concept of piecewise stationarity is how to choose the length of a segment that is neither too short for calculating statistical estimates nor too long so that the process is no longer stationary.
- the criterion for selecting the segment length should always be dependent on the method used in order to model the non-stationary process. For example, for a quasi-stationary process, the underlying assumption is that the parametric properties might change their state between different time segments. As a result, an ideal segment should not be too long to overlap segments having different parametric values.
- parameters of a time varying autoregressive model do not suddenly change, but gradually evolve along with time. Proper selection of a method to model a process depends on some basic properties of the raw data.
- a seismic wave recording or an electroencephalograph recording containing a seizure shows a sudden state change.
- a quasi-stationary method for modeling For other processes, such as the population of some species or the price of a stock, one might only be interested in their smooth evolution property instead of their sudden change due to special or dramatic events, so it would be reasonable to use a time- varying autoregressive model that will be introduced later.
- Those methods of modeling a non- stationary process are called parametric methods.
- non-parametric methods which do not assume the existence of a model or distribution family in a process. Compared to parametric methods, non-parametric methods still involve parameter choosing to some extent but not as much as parametric methods. If one intends to observe a non-stationary process as a piecewise, quasi, or evolutionary stationary process, a very well-known and widely used non-parametric tool called time-dependent spectrum in the time-frequency analysis field can be used.
- the benefits of using a parametric method are its simplicity and lucid structure.
- the main feature of parametric methods is the use of parameters as structural elements to introduce interpretation and interaction so that one can reduce ambiguity within the data itself. This, however, might be achieved at the risk of misinterpretation.
- Some other parametric approaches are based on specific assumptions that process outputs belong to the family or families of the distributions used in the model or can be described as the output of a stochastic process, whereas non-parametric approaches do not impose specific constraints with regards to the distribution family.
- Time-Varying Autoregressive (AR) models just like a stationary process, can use parametric or non-parametric means to start the analysis on a non-stationary process.
- AR Time-Varying autoregressive
- One of the most commonly used models for simulating or fitting non-stationary time series is the time-varying AR model.
- a p' h order linear time-varying AR model can be written in a general form as Equation 2-2.
- Equation 2-2 ⁇ , 4 are time-varying parameters that differentiate a time-varying AR model from an AR model that has a fixed coefficient ⁇ instead of ⁇ .
- the main difficulty in using a parametric model for analysis lies in choosing proper values for the parameters.
- Equation 2- 2 shows, p and ⁇ are parameters which need to be chosen based on the training data while 3 ⁇ 4is a zero-mean white noise process.
- One advantage of a parametric method is that it renders a lucid dynamic relationship between data points and gives some sense of how data evolve over time. However, the model may not be unique because of the uncertainty of parameters.
- models of different orders may be fit into the same datasets.
- time varying AR model parameter values ( ⁇ ⁇ ) might be significantly different especially for a complex dataset.
- Several methods have been proposed to find the optimal order of an AR model such as Akaike information criterion, Bayesian information criterion, and the likelihood ratio test. Once the order of the AR model is decided, ⁇ ⁇ are calculated from Yule- Walker equations. Other methods exist for estimating regression coefficients, such as Burg's method, least-squares approach, modified covariance method, covariance method, parametric spectral estimation method, Prony's method, etc. However, choosing the order of a time-varying AR model is more complex than that of an AR model. A recently proposed method for time- varying AR model order uncertainty is the generalized likelihood ratio test.
- ARIMA Autoregressive Integrated Moving Average
- ARIMA Autoregressive Integrated Moving Average
- An autoregressive moving average model (ARMA) can be represented in Equation 2-3.
- Equation 2-3 is a Gaussian white noise process.
- An ARIMA can exhibit not only ARMA but also non-stationarity having neither fixed mean nor fixed variance.
- a very important property of ARIMA is that if one takes the d' h derivative of the process it will result in a stationary process that can be represented by another ARMA model . This relationship can be represented in Equation 2-4.
- Tilda indicates a vector. If the transition matrix is denoted as F k , the noise coupling matrix as G k and the observation matrix as h - V-fi, ⁇ ⁇ ⁇ 0] .
- Equation 2-3 and Equation 2-4 become Equation 2-7 and Equation 2-8.
- Equation 2-9 3 ⁇ 4is a zero-mean innovation with time-varying variance and F k is described in
- Equation 2-1 1 Equation 2-1 1 .
- Non-parametric methods assume no specific distribution or fixed structure existing for a process. Some parameter settings still exist in the non-parametric methods but the parameters are mainly for the sensitivity aspects of the analysis rather than relating to whole process. As a result, non-parametric methods are less affected by the choice of assumptions or parameter value compared to a parametric method. In sum, non-parametric methods do not explain the mechanism behind a time series and are more data-driven.
- Wavelet analysis is one of the most utilized tools for time-frequency analysis. Most of the stationary processes are generated and recorded in the time domain. However, a weak stationary process can be characterized by its' frequency components. That is why Fourier transform is applied in almost every field of science and engineering. The Fourier transform represents a process formulating a superposition of frequencies.
- Equation 2-12 i denotes an imaginary unit.
- the representation through Fourier transform can clearly show those weighted components of a process in terms of frequencies, it does not include any time component. One can hardly perceive when those frequency components participate in a process.
- a functional transform showing results in both the time and frequency domain can be much more informative and intuitive.
- a very widely used time-frequency analysis is the wavelet transform which renders a perspective with both time and frequency resolutions through imposing a mask function before the original signal.
- Equation 2-14 vt'(/ - r) is a window function.
- w(t - r) is a rectangular window the above equation is also called short-time Fourier transform, windowed Fourier transform, or time- dependent Fourier transform.
- a real life signal such as seismic waves show characteristics of a short impulsive feature that can hardly be described through Fourier transform decomposing the seismic wave into a combination of sinusoidal functions ranging from negative infinity to infinity. Because of the dual property of a wavelet in both the time and frequency domain, one cannot use a wavelet for time-frequency analysis only, but also for de-nosing a process that has noise with a certain unique frequency band and that occurs sporadically along the time frame.
- second-order statistics such as variance or auto-covariance may be estimated through only a segment of observation and have confidence in the estimated statistics because its stationarity has rendered characteristic quantitative homogeneity. Having longer term observation, statistics may be estimated better through elongating the observational period.
- the variance of a process changes slowly over time, saying that variance is a continuous and differentiable function of time, the variance could still be estimated with certain precision by gathering information around the time point of interested variance. This demand exactly fits the property of wavelet transform which preserves the local characteristics of a process to some extent on both the time and frequency domain respectively.
- a statistically slowly changing process can be called a local stationary process.
- X there is a Cramer representation as Equation 2-1 5.
- Equation 2- 5 exp means exponential and Z( ⁇ a) is a stochastic process with orthonormal increments.
- Non-stationary processes can be written almost the same as Equation 2-15 but - ⁇ ( ⁇ ) j s replaced by a function of time. Following this rationale, a non-stationary process can be represented using local stationary wavelet and non-decimated discrete wavelets
- Equation 2-16 To express a local stationary process, one can write it as Equation 2-16.
- Equation 2-16 ⁇ is the mutually orthogonal zero mean random innovation. From Equation 2-15 and Equation 2-16, one should notice that w , in Equation 2-15 corresponds to ⁇ ) in Equation 2-15 and both of them indicate the amplitude of each analysis component. One should also notice thaty/ k (t) is a replacement of the Fourier harmonics tern exp(i ot) , in Equation 2- 15. The subscript indices j and k in w / .* represent scale and time location respectively just like those ⁇ ⁇ j k (t) .
- non-decimated discrete wavelet The reason for using a non-decimated discrete wavelet is that it can be shifted to any time point and not only confined in shifts of 2 " ⁇ ' compared with a discrete wavelet. Please note that non-decimated wavelets do not have orthogonalities and are an overcomplete collections of shifted vectors.
- An example of a discrete non-decimated wavelet is the Haar wavelet.
- Nason also proposed an evolutionary wavelet spectrum (EWS) to quantify how the size of w t k changes over time as in Equation 2- 7.
- EWS EWS
- S, (-) still has resolution on both the frequency and time domain but with a different time scale which rescales the whole observation time into z e (0, 1) ⁇ escaled time, z , is calculated by dividing k by the whole observation time length, T , and
- Equation 2-18 The goal is to estimate the variance of a local stationary process. To accomplish that, one way is to put together the localized information around the time point of interest, with the concept of local stationary wavelet and EWS, let C ( Z , T ) represent localized autocovariance and be defined as Equation 2-18.
- Equation 2-18 ⁇ , ⁇ ) is the autocorrelation function of ⁇ Lk (0 and [ ⁇ ] denotes the integer part of the real number.
- localized variance at time z can be defined as described in Equation 2-20.
- a Kalman filter can be used for prediction on a more parametric basis. Compared to a Kalman filter, local stationary wavelets do not necessarily need to fit data with a parametric model and may concern only measurement per se. In contrast to a parametric analysis, a non-parametric analysis forsakes the idea that there is a model governing the evolution of data and that, in any case, the observation should be allowed to characterize the data by itself.
- the Kalman filter is a recursive filter that can estimate linear dynamic parameters given some noisy measurements.
- filter should not be taken as only a passive data processing algorithm, but think of it as an active computer program that gathers information from inputs and then optimally estimates the transition of a system.
- a non-stationary process can be treated as a stationary ARMA after taking appropriate orders of derivative on the ARIMA.
- Equation 2-26 1 is the identity matrix, ⁇ is a zero-mean white noise vector. If H is defined as an identity matrix, ⁇ j s a random walk process and then 3 ⁇ 4 ends up being an integrated random walk process. If H is a zero matrix, then should be a white Gaussian noise process and 3 ⁇ 4 ends up being a random walk process. Please note that the role of j$ the first order difference of 3 ⁇ 4 and it describes the changes between and 3 ⁇ 4-i as time moves on. A non-stationary process can be predicted, which is a time-varying AR (2) model, once the crucial step of choosing parameters in the model is done and this can be
- Kalman algorithm A general way of implementation of a Kalman filter starts with setting up the parameter model in the state space form.
- LSW Local Stationary Wavelet
- an interested process can be written as X 0T ,...,X t _ r where T - t + h and then define a linear predictor using Equation 2-33.
- the next task is to optimize b ⁇ s T so that the mean square prediction error (MSPE),
- the whole procedure of forecasting a non-stationary process with long enough observations involves two training sets. First, divide the long-term observations into two training sets and use the first one to generate the B t T matrix. Second, use the other training set to optimize b ⁇ vector such that MSPE is minimized. In practice, the first part involves selection of two more parameters. Once those parameters are selected, the model would be ready for prediction.
- An epileptic seizure is a transient occurrence of signs and/or symptoms due to abnormal excessive and synchronous neuronal activity in the brain.
- the worldwide prevalence of epilepsy ranges from 0.4% to 1 %.
- Some epileptic patients experience a prodrome or an aura, which can serve as a warning before the signs of seizure onset.
- most patients cannot predict or arrest their seizures.
- about 70% of epilepsy patients are able to gain satisfactory control of their seizures. For patients whose seizures do not respond to antiepileptic medications, less than 50% are candidates for epilepsy surgery.
- the convolutional neural network outperformed logistic regression and the support vector machine.
- the best result achieved by using wavelet coherence and a convolutional neural network was 71 % sensitivity with zero false-positive rates for 15 out of 21 patients.
- two dynamic features (mean phase coherence and dynamic similarity index) were applied on 1 ,456 hours of long-term continuous intracranial EEG data from eight patients.
- the prediction sensitivity increased (from 25% to 43.2%) when they used logical "AND" combinations to join the benefits of both features.
- the method was applied on a 21.5 hour scalp EEG dataset recorded from 4 patients with temporal lobe epilepsy. They reported a training result of 87.5% sensitivity (16 seizures) with a false prediction rate of 0.28 per hour, where the average prediction time was approximately 25 minutes.
- James and Gupta analyzed long-term continuous scalp EEG recordings from nine patients (5 in training set and the other 4 in test dataset). The data were processed by a sequence of techniques consisting of independent component analysis, phase locking value, neuroscale, and Gaussian mixture model. The prediction performance of this method achieved a sensitivity of 65-100% and specificity of 65-80% as the prediction horizon ranged from 35-65 minutes in the test dataset.
- an automated seizure prediction algorithm may be constructed that monitors the change of T-index and issues a warning of an impending seizure when the T-index curve exhibits the pattern defined by the algorithm.
- T-index paired t-statistic
- the general hypothesis is that seizures are preceded by PMRS entrainment; this hypothesis was based upon findings reported previously using a different measure of signal order, STLmax.
- the prediction parameters and the specific EEG channels to be monitored were determined by the use of a training dataset. Algorithm performance was then assessed using an independent test dataset. The performance was further validated by compa son with that from a random warning scheme that did not use any information from the EEG signals.
- EEG signals were first filtered by a fifth-order Butterworth filter with a band-passing frequency between 1 to 20 Hz (the bandwidth within which most ictal epileptiform patterns occur). After the filtering process, for each channel, PMRS was calculated for each non- overlapping 5.12-second epoch. Based on the PMRS values, T-indices were then calculated for each of the selected channel groups. To increase the sensitivity of seizure warning, the proposed algorithm independently monitored four T-index curves (i.e., from four channel groups). A warning was issued when any of the monitored T-index curves met convergence criteria.
- PMRS is a probabilistic statistic quantifying signal regularity.
- One of the characteristic features of EEG signals during a seizure is the rhythmic and regular discharges over a wide range of the brain. Therefore, the first step of the warning algorithm presented in this study calculated PMRS sequentially for each EEG signal analyzed.
- the rationale of applying this pattern match method is due to its robustness over scalp signal values, which are usually more unstable than their up-and-down trends. The procedure for calculating PMRS is described below:
- Equation 3-1 the first two criteria require value match to some extent at both the beginning and ending points of two segments, where e was set to be 0.2 empirically.
- the third criterion requires pattern match between x, and x y within a range of m (set as 3 in this study).
- p a conditional probability
- p t can be estimated as p l as in Equation 3-3.
- Equation 3-3 1 ⁇ t ⁇ n - m. Finally a PMRS can be estimated.
- T-index is basically the paired t-statistic function used to quantify the degree of convergence between two PMRS time series.
- X t and X j the PMRS value time series
- their values in a calculation window W 1 with a size of n data points are presented as and L in Equation 3-5 and Equation 3-6.
- Equation 3-7 The T-index over the calculation window W t between the two time series is calculated using Equation 3-8.
- Equation 3-8 D . and a n t are the sample mean and the sample standard deviation of Df, respectively.
- PMRS convergence is a process during which one EEG signal is influenced by or coupled with another with respect to the signal regularity. This phenomenon was used as a dynamical pattern for warning of an impending seizure.
- Figure 3-1 shows the PMRS traces derived from three EEG channels (F8, T4, and T6) (upper panel) and their average T-index values (bottom panel) over a 350-minute interval containing a seizure. As shown in the PMRS plot, all PMRS values of the three channels dropped seconds after the seizure onset (indicated by a black vertical line), which was due to the extreme signal singularity during the ictal period. More importantly, the PMRS values became convergent about 60 minutes before the seizure onset, which caused the decrease of T-index values (shown in Figure 3-1 ).
- Channel groups were selected such that they were bilaterally symmetric along the midsagittal line.
- electrodes Fp1 and Fp2 were excluded.
- electrodes 01 and 02 were also excluded.
- the frontal electrodes F3 and F4 were included in the analysis, whereas electrodes F7 and F8 were not included in order to minimize muscle artifact due to chewing.
- the four channel groups selected in this study resemble the well-known and popular anterior-posterior bipolar ("double banana") montage. These four channel groups were: (F7, T3, T5), (F3, C3, P3), (F4, C4, P4), and (F8, T4, T6).
- the main rationale for this selection was that most seizures occurring in patients with temporal lobe epilepsy start from a channel group on one side (hemisphere) of the brain, and therefore, intuitively, these channels were more likely to be entrained with each other during the preictal transition period.
- the algorithm was enabled to detect a PMRS convergence that preceded an impending seizure initiated from either hemisphere.
- the window size for calculating one group T-index is 60 PMRS data points, with 59 points overlapping from t to t+1 (i.e., sliding window).
- the warning algorithm only monitored the four group T-index curves instead of individual pair-wise T-indices. Detection of PMRS convergence
- the proposed prediction algorithm instead of attempting to detect a signal threshold crossing, was set to detect a certain pattern of T-index dynamics that gradually descends from a baseline value. Therefore, the first step to detect such a pattern was to determine an upper threshold U T (i.e. , baseline value, see an illustration in Figure 3-2).
- U T i.e. , baseline value, see an illustration in Figure 3-2.
- U T For each group T-index, its U T was set to be the asymptotic 95 th percentile in the preceding 12 minutes, as described in equation 10. The duration of 12 minutes was decided by training across multiple patients in the training dataset.
- Equation 3-12 /( ⁇ ) is an indicator function, A is the criterion of updating U T , and T(t) is the group T-index value at time t. If A is false, then U T is kept as it is. ( ⁇ ) denotes the Heaviside step function.
- U T is not updated with a maximum value because the existence of artifact in raw EEG recordings could affect the T-index causing an abrupt surge and therefore produce an abnormally high U T .
- L T is equal to U T minus D, where D is a parameter that would determine the sensitivity of the algorithm. In general, the bigger D is, the less sensitive the algorithm will be, but the less susceptible the algorithm will be to false warnings.
- the algorithm would issue a warning of an impending seizure only when any of the monitored T-index curves traveled from U T to L 7- with the traveling time longer than t t to ensure a gradual descendent pattern.
- EEG segments with a tolerable level of artifact i.e. , not present for more than 50% of the recording and not involving more than 50% of the recording channels, were included in this study.
- the warning algorithm had a sufficiently long period of observation to detect the transition from interictal to ictal states.
- the total EEG recordings used in this study was 1786 hours and contained 98 seizures.
- the individual recording durations of each subject in the whole dataset are shown in Figure 3-4.
- SWH seizure warning horizon
- FPR false positive rate
- sensitivity was estimated by dividing the number of correct warnings by the total number of seizures in the EEG segments, i.e. the proportion of seizures correctly predicted (within SWH).
- FPR per hour was calculated by dividing the total number of false positives by the total recording hours outside the SWH before each seizure. The SWH period before each seizure was excluded because it was impossible for a false warning to occur within the SHW before each seizure.
- the total number of warnings allowed by the random predictor was set to be the same as that issued by the test algorithm. For example, if the test algorithm issued two true positive and two false warnings in a specific segment, the random predictor would only randomly issue a total of four warnings. Under the same number of warnings allowed, the study compared overall prediction sensitivity across all test patients. A distribution of overall sensitivity by the random prediction scheme was generated from 1000 simulations, and was used to assess how significant the prediction performance by the test algorithm was over the random scheme.
- the comparison of performance between the proposed warning algorithm and the random scheme was further implemented through cross-validation so that the comparison result is more independent from the constituents in the training dataset and test dataset.
- all 71 segments may be randomly divided into training and test datasets for 20 times to generate 20 individual trials and then repeated the training and test procedures on each trial.
- the parameters (t t and D) were selected as those causing the performance to exceed 70% sensitivity and resulting in the least FPR in the training dataset.
- the parameters were input to the test algorithm run on test dataset to generate the final performance results in the trial.
- the final performance result of the test dataset was compared with the random seizure warning scheme mentioned above.
- each test segment in each trial can have a different number of warnings and even the same segment in different trial would have a different number of warnings if the parameters used in the two trials were different.
- Using fixing parameters for a group of epileptic patients with different seizure types and physiological backgrounds can hardly outperform that using best setting parameters for each individual patient.
- these results can offer a perspective on the robustness of using the test algorithm among several patients when the previous individual patient data is not available or sufficient for training.
- the comparison result between the test algorithm and the random scheme is quantified as a p-value, and indicates how significant the prediction performance by the test algorithm was over the random scheme.
- the overall statistical significance of comparison between the two seizure prediction schemes was estimated by mapping the p-values to a z distribution.
- the z-transform method was chosen for testing combined p-values because it is not differentially sensitive to data that support or refute a common null hypothesis, whereas Fisher's test, another widely- used method for testing combined p-values, is more sensitive to data refuting a common null hypothesis.
- each ROC curve first reached its peak sensitivity and then declined as D kept increasing. This was due to the constraint of t t : when D was set to a small value, T t , the time interval during which a group T-index curve drops from U T to L T , was likely to be shorter than the minimally required t t , and therefore the drop of the group T-index curve could not be considered as a PMRS convergence. As D became bigger, the sensitivity started increasing until the D value became too large to start affecting the number of group T- index drops (i.e., sensitivity started to reduce).
- the classifier is usually optimized using a portion of the EEG segment of one patient and then tested on the rest of EEG segments from the same patient. Training parameters vary from method to method. As long as all parameters were fixed once after the training procedure ends, no more optimization or changing of parameter values should be allowed in the test process; otherwise, the result should not be viewed as an independent test result but a result of further in-sample optimized procedure. Although the dataset is divided into two parts, the further optimized result should not be viewed as an independent test result since some parameters have fixed before the further optimization.
- Table 3-1 The sensitivities, false-positive rates and p-values achieved by the proposed algorithm on training and test dataset.
- the sensitivities and FPRs of the training datasets presented in this table are the best performances, defined as reaching sensitivity over 70%, meanwhile, resulted in the least FPR.
- the sensitivities and FPRs of the test datasets resulted from applying the proposed algorithm using the best parameter configuration found using the training dataset.
- the p-values in the test datasets were estimated by comparing the test algorithm to the random warning scheme (1000 simulations in each trial) that issued the same number of warnings.
- FIG. 1 Dynamic features of three EEG electrode signals. Top: PMRS traces of F8, T4, and
- T6 electrodes There is a sudden drop of PMRS values in all three channels right after the seizure onset (denoted by vertical dashed black lines in both panels at the 200-minute time point). Bottom: averaged T-index among the three channels. Approaching the time of seizure occurrence, a gradual decrease of the T-index (convergence) from approximately the 120-min point to the 60-min point can be observed. The T-index values remain small before the seizure.
- FIG. 3-2 The group T-index plot with warning algorithm parameter indications.
- the seizure warning sensitivity relates to parameters t t and D .
- the algorithm finds both L T and U T , the difference of time and the group T-index between them , as indicated by Tt and d in the figure, are compared with t t and D, respectively. Only the decrease d of a T-index curve was larger than D , and also Tt larger than t t would trigger a seizure warning.
- the T-index drop at 100 min was not considered a warning event because a large d occurred during a short Tt.
- the T-index drop from the 120 min point to the 160 min point shows a gradual and persistent decrease and is considered a proper warning event.
- the dashed vertical line at 200 minute denoted the seizure onset time point.
- Figure 3-4 Recording duration of all 71 subjects in the dataset.
- the range of recording duration was between 6.18 to 70.25 hours.
- the mean was 25.16 hours and the standard deviation was 10. 98 hours.
- Each point in the ROC curve corresponds to an overall result over the training dataset with a specific D value.
- the inset indicates the parameter t t used in each ROC curve.
- the best parameter configuration of this training dataset was observed at the t t value equal to 20 minutes and D equal to 3, which achieved sensitivity above 0.7 with a false positive rate of 0.232 per hour.
- Figure 3-6 The performance comparisons of the 20 trial.
- the figure shows the comparisons between the performances achieved by the random scheme and that achieved by the proposed algorithm.
- the bar plot shows the histogram of the sensitivities achieved by the random warning scheme (generated from 1000 repetitions).
- the sensitivity of the proposed algorithm applied on the same test dataset is denoted by the dashed vertical line, which was better than 91.6% of the sensitivities of 1000 repetitions achieved by the random scheme.
- PNES psychogenic nonepileptic seizure
- EEG scalp electroencephalogram
- the classification using ictal symptoms requires several seizing onsets from a patient.
- the number or frequency of seizure onsets during a patient's stay in EMU cannot be precisely anticipated in advance. It would be convenient for EMU schedule and cost efficiency if one could identify PNES patients using only awake and interictal scalp EEG recordings.
- This study researched the connectivity and features of awake and relaxed interictal EEG signals.
- the subjects include seven patients having PNES and another seven patients having complex partial seizures (CPS) with fixed foci.
- a brain is a structurally and functionally complex network of neurons.
- the functional network reflects the connectedness among brain regions in terms of neuronal activity.
- Graph theoretical analysis is a mathematical tool to reveal topological characteristics of a network. Applying graph theoretical analysis on the EEG data reveals the brain functional network features.
- One of the network structures called "small-world network” can be identified, when there is a balance between local independence and global integration in the network. The balance can be evaluated by quantifying two graph features, called the local clustering coefficient and the characteristic path length.
- a small world network has a relatively high cluster coefficient and a small characteristic path length. Small world networks are usually compared to a network with a lattice-like configuration or to a random network; the two extreme cases.
- a regular lattice network is characterized by a relatively high cluster coefficient and a long average path length.
- a random network has a relatively lower cluster coefficient and a shorter average path length.
- Small-world networks are efficient at information processing, cost- effective, and are relatively resilient to network damage and, as a result, can be regarded as the ideal model for a normally functioning brain network.
- EEG data has one salient characteristic, the rhythmic oscillation.
- frequency analysis has been broadly used to preprocess and analyze EEG signals. It is widely accepted that the different strengths of the frequency components can reveal different brain states.
- the brain functional network can be represented as a graph.
- Graph theoretical analysis is then applied after the graph has been established. To do so, first define vertices and edges in the EEG data. If the EEG channels are designated as the vertices of a graph, an edge between two vertices signifies a functional connection between two EEG channels. One would expect a larger correlation between two EEG channels when there is an edge between them. Edges can also be values quantifying how well the two vertices correlate in weighted graphs.
- Most of the studies using graph theoretic analysis on EEG data assume that statistical interdependencies between EEG time series reflect functional interactions between neurons in the brain regions. There are many statistical metrics computing the degree of association between time series. Some of the most commonly used metrics in EEG functional connectivity graph studies will be discussed below.
- Phase locking value is a statistic measuring the frequency-specific synchronization between two neuroelectric signals. This is a method focusing on the phase information of time series and is different from coherence, which gives the interrelation of both amplitude and phase between signals.
- the PLI is calculated by first extracting the instantaneous phase information of signals through either wavelet transform or Hilbert transform. Both methods lead to a similar result in real world EEG data.
- a wavelet function, ⁇ ( ⁇ ) is first chosen. Gabor and Morlet wavelet functions have both been applied on EEG data. Then the wavelet coefficient time series, W x (t) can be computed by convolute x(t)and W x t).
- phase time series 0(t)
- Equation 4-4 p. v. denotes the Cauchy principal value in the equation. Then the relative phase, ⁇ (t), can be calculated as Equation 4-5.
- PLI was used in a study by Dimitriadis et al. to construct the functional connectivity graphs from 30- electrode EEG data. They utilized surrogate data to generate a baseline distribution of random PLIs and then determined the functional connections (edges) if there was a significantly different (p ⁇ 0.001 ) PLI for a specific pair. The surrogate data is generated by permuting the order of trials of one signal repeatedly.
- Synchronization likelihood is a statistic measuring the non-linear similarity between time series.
- SL offers an extended perspective of correlation that is not limited in terms of linear relationship; while coherence, has the limitation of rendering only the linear correlation as a function of frequency.
- Equation 4-7 I denotes the lag and m is the embedding dimension.
- a number l ⁇ is then defined to denote the number of channels X k i and X k j that are closer than a crucial
- SL Synchronization Likelihood
- NIM Non-linear Independent Measure
- V-conditioned mean squared Euclidean distance as Equation 4-12 but replace the nearest neighbors by the equal time partners of the closest neighbors of X kl i .
- NIM N(X ⁇ Y) .
- Phase lag index quantifies the asymmetry of the distribution of instantaneous phase differences between two time series. If the relative phase time series between channel e and f, (p eJ (t) have been calculated, then the PLAl can be defined as ⁇ (sign[(p e f (t)] ) ⁇ (( ⁇ ) signifies the expectation value operator). PLAl ranges from 0 to 1 . PLAl values greater than 0 suggest the existence of phase locking to some extent, and values equal to 0 signify no coupling or no coupling with a phase difference centered around 0 ⁇ radians. PLAl is supposed to rule out the synchronization due to instantaneous volume conduction or a common source that is the main cause giving spurious synchronization. Results of Studies Using Small-World Network Analysis to EEG Data
- Small-world networks are supposed to be very efficient for data transfer.
- Epilepsy as a disease having excessive synchronization between neurons is assumed to have a relationship with the small-world architecture in the functional brain network.
- Ponten et al. conducted a study doing graph analysis on intracerebral EEG recordings from patients having drug-resistant mesial temporal lobe epilepsy and found an increase in the clustering coefficient in the lower frequency band (1-13 Hz), and an increase in the path length in the alpha and theta bands during and after a seizure compared to interictal recordings. This implies that the functional brain network changes from a more random organization to a small-world structure.
- AD Alzheimer's disease
- Boersma ef al. conducted a study on resting state EEG in developing young brains. They recorded resting-state eyes-closed EEG (14 channels) from 227 childern when they were 5 and 7 years of age and found out that the clustering coefficient increased in the alpha band with age. Path lengths increased in all frequency bands with age. This suggests that a brain shifts from random towards more ordered, small-world like configurations during maturation. Girls showed higher mean clustering coefficients in the alpha and beta bands compared with boys.
- Schizophrenia has been suspected as the result of a more disconnected brain network among certain crucial areas in the brain. Rubinov et al. did a study investigating the
- connection hypothesis They recorded resting state scalp EEG from 40 subjects with a recent first episode of schizophrenia and another 40 healthy matched controls. Nonlinear interdependences were identified from bipolar derivations of EEG data and weighted graphs were generated. Graphs of both groups showed features consistent with a small-world topology, but graphs in the schizophrenia group displayed lower clustering and shorter path lengths. This result can be interpreted as a pathological process that the small-world network transformed to a more randomized small-world network in a schizophrenia brain. This randomization may be the reason why schizophrenia evidences cognitive and behavioral disturbances.
- the symmetric parts of a human body such as limbs and sense organs, often have the same function and structure.
- the brain of a human also has symmetric shape although some functions happen on a dominant side.
- the EEG signals from a pair of symmetric channels usually have similar morphologies.
- the asymmetry of EEG signals is regarded as a pathological consequence or unusual phenomenon if the reason is not found.
- Many studies have used asymmetry as an index to quantify the morbidity of brain disease or abnormal states. In this study, the hypothesis is that the relative frequency powers of symmetric pairs of EEG channels are more different in CPS patients than that in PNES patients.
- the powers of EEG signals in narrow frequency bands associate with different brain functions or motifs.
- the degree of asymmetry is quantified through the relative frequency power of several frequency bands and the T-index, a statistic measuring the degree of divergence between two groups.
- the EEG signals of each subject were reviewed to select out the awake and relaxed state sections containing the dominant alpha waves over the occipital regions and no eye-blinking events around the frontal electrodes.
- the awake and relaxed state EEG signals containing epileptiform discharges or other suspicious epileptic activities were also excluded. All selected awake and relaxed state sections were at least five hours before the first CPS or PNES happened.
- the brain is supposed to be in a resting state and not actively involved in any goal-oriented events.
- the awake and relaxed states offer controlled background for the brain network to be compared between subjects.
- an awake and alert section of long-term continuous EEG from different patients could contain a variety of ongoing
- oscillation frequency is a main characteristic of the brain and changes when the brain undergoes different psychological conditions or executes different cognitive tasks
- all selected epochs were filtered to specific frequency bands including delta, theta, alpha, and beta. All signals were filtered using filters that do not distort the phase information of the filtered signals so that the instantaneous phase time series of the original and filtered signals are the same. This is crucial for this analysis because the connection strength was evaluated using phase information solely.
- PLAI was estimated in every five-second epoch of all selected awake and relaxed state sections.
- a weighted graph representing the functional network can be generated after all pair- wise PLAI are calculated amongst all electrodes.
- the weighted graph can also be presented as a weighted adjacency matrix as in Figure 4-3.
- a threshold can be chosen and applied to all PLAI values such that the edges between vertices is either connected or disconnected. The choice of threshold is done by controlling the density of a graph so that the non trivial structure of the network can be revealed.
- the threshold in each epoch can be different from each other and is increased slightly from a small value until the desired density of a graph is reached.
- the threshold changes from epoch to epoch because the brain may undergo many phases of signal processing and show different connection strength between functional regions while the structure of the information flow should persist in a small-world configuration so that the information is efficiently shared and processed among functional regions. For different subjects, it is reasonable to have individual thresholds for each epoch so that the dominant structure of the functional network can be revealed and compared across subjects.
- a network measure is a value quantifying a characteristic of the topology of a network.
- a clustering coefficient and minimum path length are two crucial measures to evaluate how small-world a network is.
- a clustering coefficient quantifies how locally entangled a network is, and a minimum path length reflects how globally integrated a network is.
- the local clustering coefficient can be calculated as Equation 4-14.
- the clustering coefficient, Cp is the average of local clustering coefficients of every vertices in the graph as V is the number of vertices in the graph.
- Equation 4-16 m i; is the shortest path length from vertex i to vertex /.
- the ratio of Cp/ ⁇ Cp-s> to Lp/ ⁇ Lp-s> is called the small-world network index, ⁇ . If ⁇ >1 , it is suffices to claim that the investigated functional network is a small-world network because the investigated network possesses a higher clustering coefficient or lower minimum path length comparing to 100 randomized networks possessing the same number of edges and vertices.
- Frequency power density, X(f), can be estimated by applying discrete Fourier transform on the interesting time series, x ⁇ t) .
- the alpha band relative power would be the ratio of the sum of powers in the alpha band to the sum of powers from 1-58Hz.
- These ratios, rp were further transformed to a variable, rp', as described in Equation 4-18 so that rp' has a distribution close to the normal distribution
- T-index is a function to compute the degree of divergence between paired-samples from two groups.
- sample groups were the relative powers of a certain frequency band from an anatomically symmetric, left and right, pair.
- Left and right relative powers in each epoch should be paired up because they both reflected the state of the brain during the same period of time.
- D LR is the mean of the differences of relative powers, rp', of each awake and relaxed state EEG epoch and ⁇ ⁇ is the standard deviation of the differences. Due to the fact that each subject has a different length of awake and relaxed state EEG recordings, and the number of samples (degree of freedom), n, for calculating T-index should be fixed so that the comparison is meaningful, random sampling was performed for each subject so that each subject has 36 (9 random samples from 4 continuous awake and relaxed state EEG segments) epochs input to the T-index function.
- one functional network graph was generated after the PLAIs were estimated pair by pair.
- the clustering coefficient, minimum path length, and small-world index was calculated from the adjacency matrix. All network measures of every epoch from a patient were averaged into one value for each network measure. As a result, every subject has one final value for each network measure. Totally, the PNES or CPS patients group has seven subjects and therefore, seven values for each network measure.
- the small-world index, ⁇ is larger than 1 in all frequency bands for both patient groups, supporting the existence of a small-world network structure in both groups in all frequency bands.
- a Student T-test was performed to test if the ⁇ in CPS or PNES patient group was larger than one.
- the inter-hemispheric power asymmetry was quantified by Tind LR .
- the means of Tind LR of every pair (besides T5-T6) in the CPS group were larger than that of the PNES group.
- the beta band the means of Tind LR of every pair (besides P3- P4) in the CPS group were larger than that of the PNES group.
- the gamma band the means of Tind LR of every pair in the CPS group were larger than that of the PNES group. Almost every anatomically symmetric pair in the CPS patient group showed more power asymmetry than that in the PNES patient group.
- ANOVA Analysis of variance partitions an observed variance into several components of some possible factors and provides a test of whether the means of groups are equal. It was hypothesized that the variance of the T-indexes, which quantify the inter-hemispheric asymmetry, can be partitioned into components explained by patient groups, pairs and frequency bands. Two-way ANOVA considers two factors in a linear model to explain the interesting dependent variable, and tests if the means of factor groups are the same. Amongst three factors, the main interest is to test if the patient group is a strong factor explaining the variance of the T-index. The patient groups and anatomically symmetric pairs were first chosen as potential factors for explaining the variance of T-indexes in the two-way ANOVA for each frequency band.
- results showed that patient groups were the significant factor in the T- indexes, and the T-indexes were significantly different between the two patient groups under all frequency bands except the beta band.
- the ANOVA p-values are presented in Table 4-5.
- the patient groups and frequency bands were later used as factors and did the two-way ANOVA again for each anatomically symmetric pair.
- the results are presented in Table 4-6 and show that the patient group was a significant factor explaining the variance of T-index for those anatomically symmetric pairs in the frontal brain area.
- the global network structure and specific symmetric pair connections were investigated in both PNES and CPS EEG recordings.
- the small-world network index indicates how small-world a graph is comparing to relatively random graphs having the same number of vertices and edges.
- the small-world index was always bigger than 1 and the Student's T-test showed significance in all frequency bands for both patient groups.
- the epileptic brain functional network showed higher global integration and could possibly facilitate the generation of seizures or the secondary generalization during sleep. This study did not include any sleep EEG data so the hypothesis should be further pursued. Other network measures did not show that significant differences could result from several reasons and the possible combination of these reasons.
- the pathological network structure may not manifest during the interictal awake and relaxed state of a patient.
- the metric of association (PLAI) may not be sensitive enough to differentiate the pathological nuance of neuronal interaction.
- the network structure of the brain itself may be attack-tolerant.
- Inter-hemispheric power asymmetry is a more specific and local measure to investigate the quality of connection between hemispheres.
- the brain tissue around the foci could be damaged by the recurrent onsets of partial seizures.
- the lesion of the brain tissue should affect the ensemble neuronal activity and cause the EEG signal to deviate from the EEG signal of the anatomically symmetric channel.
- PNES patients have more similarity between EEG signals from anatomically symmetric channels due to symmetrically commensurate tissue integrity.
- the fixed focal hemisphere of partial seizures could result from substantially different pathological structures within the hemisphere. If both of the abovementioned causes are valid and additive, the asymmetry could exacerbate.
- Table 4-1 Small-world network index, ⁇ , of functional networks of CPS and PNES patients during awake and relaxed state.
- Figure 4-3 A weighted adjacency matrix.
- the matrix has 18 rows and 19 columns.
- the adjacency matrix is supposed to be a square symmetric matrix. To eliminate the redundant information, the last row is eliminated and the diagonal as well as the lower triangular part of the original adjacency matrix are forced to be zero.
- An adjacency matrix after applying a threshold on the weighted adjacency matrix in Figure 4-3 The matrix has 18 rows and 19 columns.
- the adjacency matrix is supposed to be a square symmetric matrix. To eliminate the redundant information, the last row is eliminated and the diagonal as well as the lower triangular part of the original adjacency matrix are forced to be zero.
- the threshold is applied and the entries in the matrix are either one or zero.
- FIG. 4-7 Tind LR of individual anatomically symmetric pairs in the alpha frequency band.
- Neocortical seizures originate in the neocortex—the external surface part of the cerebral hemispheres.
- Neocortical epilepsy differs from mesial temporal epilepsy in that it is difficult to clearly define a single area from which the seizures originate. Since seizures associated with neocortical epilepsy generally do not respond well to medication, epilepsy surgery is often one of the few options that patients with neocortical epilepsy have. However, surgery for neocortical epilepsy has a significantly lower success rate than other kinds of epilepsy. In patients with other types of epilepsy, such as mesial temporal lobe epilepsy (MTLE), surgeries can provide seizure freedom in more than 70 to 90% of cases.
- MTLE mesial temporal lobe epilepsy
- neocortical epilepsy Possible reasons that could result in the low success rate of neocortical epilepsy are: (1 ) there may be multiple seizure onset zones, (2) the initiation site may vary from seizure to seizure, and (3) with currently available technologies, it is difficult to precisely identify the duration and extent of seizure onset zones.
- a recent study by Lee ef al, in 2005 on nonlesional neocortical epilepsy showed that, based on the epileptogenic focus locations, only 47 out of 89 patients were seizure-free (Engel Class I) after the surgery, and an additional 7 experienced significant reduction in seizure frequency (Engel Class II). Therefore, developing a more reliable and effective method for identifying suitable parts and critical regions for neocortical epilepsy surgery would be a major contribution to improve the service of medicare and quality of life for those patients.
- MRI magnetic resonance imaging
- EEG epidermal growth factor
- Intracranial EEGs provides the most convincing evidence to support the network hypothesis. Because the entire network participates in the expression of the seizure activity and can be entrained from any of its various parts, initial electrical events (at "seizure onset”) may vary in their specific location of expression and occurrence within the network. The initial area of apparent seizure involvement is not really an onset area, because "onset” could be expressed at any place in the network, and might even vary from seizure to seizure in a given patient. This locational variability may produce different morphologies of "seizure onset" when EEG recording is performed in only one part of the network. This may be the main reason for surgical failure in the neocortical epilepsy.
- a reliable quantitative method based on intracranial EEGs for determining the spatial distribution of the nodes of the epileptic network may lead to a better understanding of the mechanisms that lead to the generation of a seizure, and provide insights into more effective approaches to seizure control.
- Two EEG segments were cut and used to construct a brain network from a continuous EEG recording containing one neocortical epilepsy seizure from the patient.
- the seizure events were identified by the recording facility based on both clinical observation and a review of the EEG. In order to avoid the potential overlapping between ictal, postictal and preictal stages, only seizures that were at least 2 hours apart from the previous or next one were used.
- the two segments analyzed were both 50 min long. One contained a seizure starting at 120 min and the other was seizure free. For the later, the previous or the next seizure happened at least 5 hours away from the beginning or ending of the seizure free segment. Both segments were preprocessed with a band-pass filter (1-220 Hz) and several notch filters (60 Hz, 120 Hz, and 180 Hz) to remove the alias, power line artifacts and DC component.
- a band-pass filter 1-220 Hz
- notch filters 60 Hz, 120 Hz
- each electrode was treated (channel) as a node (vertex) in the network and cross-correlation functions were used to calculate the weighting on the edge of each pair of nodes.
- cross-correlation functions were used to calculate the weighting on the edge of each pair of nodes.
- the brain network was constructed as follows. Both 150-minute segments were further chopped into non-overlapping calculation windows of 6 seconds to construct transient brain networks. In every calculation window, each electrode was treated as a node in the network. Pair-wire cross-correlation coefficients were calculated among all 44 nodes. A cross-correlation coefficient, r(d) , with delay d, was calculated as Equation 5-1.
- x(i ) and y(v) are EEG signal values of a pair of electrodes at time v and N is the number of sampling points in each 6-second calculation window.
- the cross-correlation coefficients with various delay d range from - 1 to +1 second) were calculated. Then, the maximum of the absolute value of the cross-correlation coefficient was obtained by selecting delay d. For each pair of nodes p and q, the weight of edge e v q is defined by this maximum value. In this way, one obtains a weighted network. To convert it to a binary network, only the edges with a weight higher than a threshold (0.9) stay in the network.
- N nodes is the total number of nodes implanted under the scalp and equals 44 for this neocortical epilepsy patient.
- the five-minute mean occurrences of degree of node x, £>x 5- m in) . was calculated and then an average degree over all nodes, AveD was calculated by averaging 3 ⁇ 4( 5 - m i n ) over all channels as Equation 5-6.
- the functional epileptic network was constructed.
- degree is one of the most widely-used basic properties of network analysis.
- AveD the connectivity of an instant network was defined as the average degree of all nodes during a five minute period and quantified as AveD .
- the regression slope of the segment with an onset is larger than zero, while the segment without any onset is less than zero. This suggested that the connectivity increases before an onset. Although the interictal segment had high values of AveD around the 95 minute, the regression slope was not larger than zero. Based on this observation, the following can be concluded. If the recording is done during interictal state, the connectivity should fluctuate within a range and have a regression slope around zero. If one has a preictal recording, one should more likely detect a positive regression slope within a period right before the seizure onset. The p-value provides information about how unlikely the regression slope is compared to the value of zero. The regression slope equal to zero means that the connectivity does not correlate with the time within the segment. This is also what was presumed to happen during an interictal state. Additional support for this hypothesis is the result that the p-value is equal to 0.0028 ( ⁇ 0.05) in the segment preceding an onset and 0.447 (>0.05) in the interictal segment.
- An epileptic seizure can be interpreted as an activity during which the neurons from different region overly correlate with each other. Therefore, one should observe a decrease of connectivity after a seizure.
- the results of this pilot study suggest that transitions in the brain networks may exist and are related to the underlying dynamics of seizures caused by neocortical epilepsy. An increase of connectivity can be observed before seizure onset. The onset of a seizure can cause the reset of the
- FIG. 5-1 Electrode placement of the neocortical epilepsy patient. There were totally 44 electrodes placed on the left frontal cortex of the subject.
- FIG. 5-2 AveD of the segment with a seizure onset at the 120 minute.
- the blue line denotes the trajectory of the connectivity states for every five minutes. Least square linear regression was implemented and the result is indicated as the red line.
- AveD of the segment without any seizure activity The blue line denotes the trajectory of the connectivity states for every five minutes. Least square linear regression was implemented and the result is indicated as the red line.
- Figure 5-4 Averaged degree over 300 calculation windows of nodes in the network. It includes five periods: 120-90 min before; 90-60 min before; 60-30 min before; 30-0 min (seizure onset) before; 0-30 min after seizure onset. Red lines separate different periods. In each period, all the 44 nodes (electrodes) in the network were plotted in bars. The height of each bar denotes the averaged degree of the corresponding node.
- AveD Average of AveD over 30 minutes before and after a seizure onset.
- the error bars indicate the standard error of the mean.
- the p-value is 0.027( ⁇ 0.05) if it is assumed that the values of AveD should be the same within 30 minutes before and after the seizure onset.
- Figure 5-6 The average of AveD over 30 minutes before and after an imaginary seizure onset that is located at 120-minute point.
- the error bars indicate the standard error of the mean.
- the p-value is 0.366(>0.05) if it is assumed that the values of AveD should be the same within 30 minutes
- the focus here was on evaluating an automated seizure prediction algorithm that issues seizure warnings by monitoring the convergence of signal regularity among EEG channels in continuous long-term scalp EEG recordings.
- the algorithm was optimized with a training dataset and its' performance was evaluated using a separate test dataset.
- the algorithm achieved an average sensitivity of 65% (i.e., ⁇ 2 out of every 3 seizures) with an average false positive rate of 0.24 per hour ( ⁇ 1 per 4 hours).
- the algorithm performance in the test dataset was nearly the same as that in the training dataset. This implies that the algorithm generated a stable performance in epileptic patients.
- the performance of the algorithm may not yet be sufficient for some clinical applications.
- the performance would be of limited utility for inpatient monitoring applications, such as the EMU setting, due to the high false positive rate.
- the performance may be useful for driving seizure control devices, such as the vagus nerve stimulator.
- fine tuning the prediction algorithm to optimize performance for each individual patient could yield even better performance.
- the performance was not yet sufficient for its usage in a clinical environment, the results demonstrated the supremacy of the algorithm compared to a random scheme. This implied that the method found some events preceding the onsets of seizures. Further analysis needs to follow to be more specific about the positive findings in this study.
- Nonlinear and univariate vs. bivariate features have been popular since 1999 but progress since then has not been substantial.
- linear methods such as the AR model or coherence have still been used and have generated satisfactory results in many EEG research fields including seizure prediction.
- Different features explain the same signal from different perspectives and should be clearly correlated to the raw signal so that one can better utilize a feature at the proper time for a suitable purpose.
- additional engineering methods could benefit the prediction scheme in the preparation and post- feature stages. In the preparation stage, filtering, inverse source locating, and network analysis could help extract more seizure-relevant information from the EEG signals before the dynamic features are applied to the signals.
- a decision to issue a warning or an index denoting the susceptibility of having a seizure should be output.
- a decider should be designed to consider situational information about the different features from the patient and integrate them in an optimal way. Optimization skills could be involved to assist in the decision process.
- a prediction scheme with an updating threshold or a learning classifier would be more adaptive to the possibly changing background of EEG activities if one considers applying the prediction scheme in an ambulant environment.
- the delta-band minimum path length was significantly smaller in the CPS patient group. This implied that the low frequency global integration was more efficient in CPS than in PNES patients. Both groups had the same small-world network indexes and clustering coefficients. These results implied that the brain either somehow maintained the structure of a small-world network or the original small-world network was attack-tolerant so that the pathological influence of epileptic discharges did not bring down the small-world configuration. The results above viewed the connection in a comprehensive scope over the whole brain.
- This selection criterion forced the presence of high alpha power in all segments and may have reduced the power of the statistical test.
- Some EEG studies in other fields also focus on power asymmetry only for the frontal region. Future research for this study could involve applying a classifier to distinguish if a subject is a CPS or PNES patient by analyzing only a short period of the awake and relaxed state EEG. This would greatly decrease the recording time and resources of an EMU. Due to the requirement that a CPS patient should receive anti-epileptic treatment, the classifier should be designed to preclude misdiagnosing a CPS patient as a PNES patient, but could be permitted to incorrectly identify a few PNES patients as CPS patients.
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